Search: a289509 -id:a289509
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A318979
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Number of divisors of n with relatively prime prime indices, meaning they belong to A289509.
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+20
3
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0, 1, 0, 2, 0, 2, 0, 3, 0, 2, 0, 4, 0, 2, 1, 4, 0, 3, 0, 4, 0, 2, 0, 6, 0, 2, 0, 4, 0, 5, 0, 5, 1, 2, 1, 6, 0, 2, 0, 6, 0, 4, 0, 4, 2, 2, 0, 8, 0, 3, 1, 4, 0, 4, 1, 6, 0, 2, 0, 9, 0, 2, 0, 6, 0, 5, 0, 4, 1, 5, 0, 9, 0, 2, 2, 4, 1, 4, 0, 8, 0, 2, 0, 8, 1, 2, 0
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A320439
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Number of factorizations of n into factors > 1 where each factor's prime indices are relatively prime. Number of factorizations of n using elements of A289509.
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+20
2
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1, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 1, 5, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 2, 0, 7, 1, 1, 1, 3, 0, 1, 0, 4, 0, 1, 0, 2, 1, 1, 0, 7, 0, 1, 1, 2, 0, 1, 1, 4, 0, 1, 0, 5, 0, 1, 0, 11, 0, 2, 0, 2, 1, 2, 0, 6, 0, 1, 1, 2, 1, 1, 0, 7, 0, 1, 0, 3, 1, 1, 0
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A327532
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Indicator function for numbers whose prime indices are relatively prime (A289509).
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+20
0
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0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0
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A327533
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Number of factorizations of the n-th number that is 1 or whose prime indices are relatively prime A289509(n - 1) into numbers > 1 satisfying the same conditions.
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+20
0
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1, 1, 2, 1, 3, 1, 2, 1, 1, 5, 1, 2, 1, 4, 1, 2, 2, 7, 1, 1, 1, 3, 1, 4, 1, 2, 1, 1, 7, 1, 1, 2, 1, 1, 4, 1, 5, 1, 11, 2, 2, 1, 2, 6, 1, 1, 2, 1, 1, 7, 1, 3, 1, 1, 4, 3, 2, 1, 1, 1, 12, 1, 1, 3, 2, 4, 1, 1, 3, 2, 7, 1, 2, 1, 1, 10, 1, 1, 2, 1, 15, 1, 5, 1, 1, 4
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A000027
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The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.
(Formerly M0472 N0173)
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+10
2086
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77
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A316413
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Heinz numbers of integer partitions whose length divides their sum.
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+10
197
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2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 17, 19, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 34, 37, 39, 41, 43, 46, 47, 49, 53, 55, 57, 59, 61, 62, 64, 67, 68, 71, 73, 78, 79, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 94, 97, 98, 99, 100, 101, 103, 105, 107, 109, 110
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A072774
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Powers of squarefree numbers.
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+10
121
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97
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A326567
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Numerator of the average of the multiset of prime indices of n.
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+10
120
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1, 2, 1, 3, 3, 4, 1, 2, 2, 5, 4, 6, 5, 5, 1, 7, 5, 8, 5, 3, 3, 9, 5, 3, 7, 2, 2, 10, 2, 11, 1, 7, 4, 7, 3, 12, 9, 4, 3, 13, 7, 14, 7, 7, 5, 15, 6, 4, 7, 9, 8, 16, 7, 4, 7, 5, 11, 17, 7, 18, 6, 8, 1, 9, 8, 19, 3, 11, 8, 20, 7, 21, 13, 8, 10, 9, 3, 22, 7, 2, 7
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A326568
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Denominator of the average of the multiset of prime indices of n.
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+10
120
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1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 2, 1, 1, 3, 1, 3, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 3, 1, 3, 3, 1, 1, 5, 1, 3, 2, 3, 1, 4, 1, 4, 1, 2, 1, 4, 1, 1, 3, 1, 2, 3, 1, 1, 2, 3, 1, 5, 1, 2, 3, 3, 2, 1, 1, 5, 1, 1, 1, 1, 1, 2, 1, 1
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A051424
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Number of partitions of n into pairwise relatively prime parts.
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+10
98
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1, 1, 2, 3, 4, 6, 7, 10, 12, 15, 18, 23, 27, 33, 38, 43, 51, 60, 70, 81, 92, 102, 116, 134, 153, 171, 191, 211, 236, 266, 301, 335, 367, 399, 442, 485, 542, 598, 649, 704, 771, 849, 936, 1023, 1103, 1185, 1282, 1407, 1535, 1662, 1790, 1917, 2063, 2245, 2436
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