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URL: https://oeis.org/A387057

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A387057
Numbers k that are infinitarily divisible by the number of infinitary divisors of k.
2
1, 2, 8, 12, 20, 24, 28, 36, 40, 44, 52, 56, 64, 68, 72, 76, 88, 92, 100, 104, 116, 124, 128, 136, 148, 152, 164, 172, 184, 188, 196, 200, 212, 232, 236, 244, 248, 268, 284, 292, 296, 316, 324, 328, 332, 344, 356, 376, 384, 388, 392, 404, 412, 424, 428, 436, 452
OFFSET
1,2
COMMENTS
Numbers k such that A037445(k) is an infinitary divisor of k.
This sequence is infinite. For example, if p is an odd prime, then 8*p is a term.
LINKS
MATHEMATICA
infDivQ[n_, 1] = True; infDivQ[n_, d_] := BitAnd[IntegerExponent[n, First /@ (fct = FactorInteger[d])], (e = Last /@ fct)] == e;
f[p_, e_] := 2^DigitCount[e, 2, 1]; id[1] = 1; id[n_] := Times @@ f @@@ FactorInteger[n]; q[k_] := Module[{d = id[k]}, Divisible[k, d] && infDivQ[k, d]]; Select[Range[500], q]
PROG
(PARI) isidiv(d, f) = {if (d==1, return (1)); for (k=1, #f~, bne = binary(f[k, 2]); bde = binary(valuation(d, f[k, 1])); if (#bde < #bne, bde = concat(vector(#bne-#bde), bde)); for (j=1, #bne, if (! bne[j] && bde[j], return (0)); ); ); return (1); } \\ Michel Marcus at A077609
isok(k) = {my(f = factor(k), id = vecprod(apply(x -> 2^hammingweight(x), f[, 2]))); !(k % id) && isidiv(id, f); }
CROSSREFS
Subsequence of A387056.
Sequence in context: A099418 A108987 A035405 * A280867 A111058 A063622
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 15 2025
STATUS
approved