A346100 -id:A346100

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Search: a346100 -id:a346100

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A346090

Numbers k such that k and A346098(k) are relatively prime; positions of ones in A346099, positions of zeros in A346100.

+20
2

1, 8, 9, 16, 18, 25, 36, 40, 42, 45, 48, 49, 50, 60, 63, 70, 77, 80, 81, 84, 90, 91, 96, 98, 100, 115, 117, 119, 120, 125, 126, 128, 133, 135, 140, 144, 147, 150, 154, 160, 161, 162, 165, 168, 169, 170, 180, 192, 195, 196, 209, 220, 221, 228, 230, 234, 238, 242, 250, 255, 256, 259, 260, 266, 270, 273, 288, 294, 297, 308, 315 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	LINKS	`Table of n, a(n) for n=1..71.`
	CROSSREFS	`Positions of ones in A346099, positions of zeros in A346100.`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jul 07 2021`
	STATUS	`approved`

A346099

a(n) = gcd(n, A346098(n)).

+10
4

1, 2, 3, 4, 5, 3, 7, 1, 1, 5, 11, 3, 13, 7, 5, 1, 17, 1, 19, 5, 7, 11, 23, 3, 1, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 1, 37, 19, 13, 1, 41, 1, 43, 11, 1, 23, 47, 1, 1, 1, 17, 13, 53, 9, 11, 7, 19, 29, 59, 1, 61, 31, 1, 4, 13, 11, 67, 17, 23, 1, 71, 3, 73, 37, 25, 19, 1, 13, 79, 1, 1, 41, 83, 1, 17, 43, 29, 11, 89 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`Only powers of primes (A000961) occur as terms. A346100 lists the exponents.`
	LINKS	`Table of n, a(n) for n=1..89.` `Index entries for sequences computed from indices in prime factorization` `Index entries for sequences related to primorial base` `Index entries for sequences related to primorial numbers`
	FORMULA	`a(n) = gcd(n, A346098(n)) = gcd(n, A064989(A319626(A324886(n)))).`
	PROG	`(PARI)` `A064989(n) = { my(f = factor(n)); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };` `A319626(n) = (n / gcd(n, A064989(n)));` `A346099(n) = gcd(n, A064989(A319626(A324886(n)))); \\ Rest of program in A324886.`
	CROSSREFS	`Cf. A000961, A064989, A319626, A324886, A346095, A346096, A346097, A346098, A346100.` `Cf. A346090 (positions of ones).`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jul 07 2021`
	STATUS	`approved`

A346087

a(n) = min(A071178(n), A329348(n)).

+10
3

0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,4`
	COMMENTS	`Each term of A345941 is a power of the greatest prime factor of n, a(n) is the exponent of that term: a(n) = A100995(A345941(n)).` `Values 0..5 occur for the first time at n = 1, 2, 4, 108, 324, 9375.`
	LINKS	`Table of n, a(n) for n=1..108.` `Index entries for sequences computed from indices in prime factorization` `Index entries for sequences related to primorial base` `Index entries for sequences related to primorial numbers`
	FORMULA	`a(n) = min(A071178(n), A329348(n)).` `a(n) = A100995(A345941(n)).` `For all n >= 1, A006530(n)^a(n) = A345941(n).`
	PROG	`(PARI)` `A345941(n) = gcd(n, A329044(n));` `A346087(n) = isprimepower(A345941(n)); \\ Rest of program given in A329044.`
	CROSSREFS	`Cf. A006530, A100995, A071178, A324886, A329044, A329348, A345941, A346100.`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jul 07 2021`
	STATUS	`approved`

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Last modified August 30 00:57 EDT 2024. Contains 375520 sequences. (Running on oeis4.)