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

1,1

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

Table of n, a(n) for n=1..53.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

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 *)

Prog

(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))));

Crossrefs

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

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

Sequence in context: A110013 A374289 A109861 * A106564 A308177 A104777

Adjacent sequences: A348751 A348752 A348753 * A348755 A348756 A348757

Keyword

nonn

Author

Antti Karttunen, Nov 04 2021

Status

approved