A364131 Numbers k for which A348717(k) is a multiple of A348717(sigma(k)).

1, 2, 4, 9, 16, 25, 64, 81, 289, 324, 400, 484, 729, 1681, 2401, 3481, 4096, 5041, 7921, 10201, 15625, 17161, 27889, 28561, 29929, 39204, 65536, 83521, 85849, 146689, 262144, 279841, 458329, 491401, 531441, 552049, 579121, 597529, 683929, 703921, 707281, 734449, 829921, 1190281, 1203409, 1352569, 1394761, 1423249, 1481089

Offset

1,2

Comments

Conjecture: All terms apart from a(2) = 2 are squares.

Links

Table of n, a(n) for n=1..49.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Prog

(PARI)
A348717(n) = { my(f=factor(n)); if(#f~>0, my(pi1=primepi(f[1, 1])); for(k=1, #f~, f[k, 1] = prime(primepi(f[k, 1])-pi1+1))); factorback(f); }; \\ From A348717
isA364131(n) = !(A348717(n)%A348717(sigma(n)));

Crossrefs

Cf. A000203, A008848, A023194 (subsequence), A348717, A350072.

Sequence in context: A006474 A110878 A253849 * A077137 A023194 A114080

Adjacent sequences: A364128 A364129 A364130 * A364132 A364133 A364134

Keyword

nonn

Author

Antti Karttunen, Jul 11 2023

Status

approved