A348754 Numbers k congruent to 1 or 5 mod 6, for which A064989(A064989(sigma(k))) > A064989(A064989(k)), where A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.

25, 49, 121, 169, 175, 275, 289, 325, 625, 841, 925, 1225, 1445, 1525, 1675, 1681, 1825, 2401, 3025, 3125, 3481, 3757, 3925, 4075, 4225, 4375, 4825, 5041, 5275, 5929, 6125, 6875, 6925, 7075, 7225, 7825, 7921, 8125, 8275, 8281, 9025, 9925, 10201, 10525, 10625, 10693, 11425, 11875, 12005, 12025, 13075, 13225, 13475

Offset: 1

Author

Antti Karttunen, Nov 04 2021

Keywords

• nonn

Comments

Sequence A003961(A003961(A348752(n))), n=1.., sorted into ascending order.

Not a subsequence of A348749. The first terms that occur here but not there are: 169, 175, 275, 1675, 3757, 4075, 5275, 7075, 8275, 10693, 12025, ...

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A003961, A007310, A064989, A348750, A348752, A348753.

Cf. also A348749, A348932, A348936 (square roots of squares present).

Programs

Mathematica

f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[15000], MemberQ[{1, 5}, Mod[#, 6]] && s[s[DivisorSigma[1, #]]] > s[s[#]] &] (* Amiram Eldar, Nov 04 2021 *)

PARI

A064989(n) = {my(f); 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)};
isA348754(n) = ((n%2)&&(n%3)&&(A064989(A064989(sigma(n))) > A064989(A064989(n))));