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A324847
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Numbers divisible by at least one of their prime indices.
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19
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2, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 55, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110, 112, 114, 116
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OFFSET
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1,1
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n.
If n is in the sequence, then so are all multiples of n. - Robert Israel, Mar 19 2019
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
10: {1,3}
12: {1,1,2}
14: {1,4}
15: {2,3}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
22: {1,5}
24: {1,1,1,2}
26: {1,6}
28: {1,1,4}
30: {1,2,3}
32: {1,1,1,1,1}
34: {1,7}
36: {1,1,2,2}
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MAPLE
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filter:= proc(n) local F;
F:= map(numtheory:-pi, numtheory:-factorset(n));
ormap(t -> n mod t = 0, F);
end proc:
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MATHEMATICA
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Select[Range[100], Or@@Cases[If[#==1, {}, FactorInteger[#]], {p_, _}:>Divisible[#, PrimePi[p]]]&]
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PROG
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(PARI) isok(n) = {my(f = factor(n)[, 1]); for (k=1, #f, if (!(n % primepi(f[k])), return (1)); ); return (0); } \\ Michel Marcus, Mar 19 2019
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CROSSREFS
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Cf. A324695, A324741, A324743, A324847, A324756, A324758, A324765, A324848, A324849, A324850, A324852, A324853.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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