A351554 Numbers k such that there are no odd prime factors p of k such that p would not divide A003961(k) and the valuation(k, p) would be different from valuation(sigma(k), p), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.

1, 2, 3, 6, 7, 10, 14, 15, 20, 21, 22, 24, 27, 28, 30, 31, 33, 34, 40, 42, 46, 54, 57, 60, 62, 66, 69, 70, 84, 87, 91, 93, 94, 102, 105, 106, 110, 114, 120, 127, 130, 138, 140, 141, 142, 154, 160, 168, 170, 174, 177, 182, 186, 189, 190, 195, 198, 210, 214, 216, 217, 220, 224, 230, 231, 237, 238, 254, 260, 264, 270, 273

Offset

1,2

Comments

Numbers k for which A351555(k) = 0. This is a necessary condition for the terms of A349169 and of A349745, therefore they are subsequences of this sequence.

All six known 3-perfect numbers (A005820) are included in this sequence.

All 65 known 5-multiperfects (A046060) are included in this sequence.

Moreover, all multiperfect numbers (A007691) seem to be in this sequence.

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351555(n) = { my(s=sigma(n), f=factor(s), u=A003961(n)); sum(k=1, #f~, if((f[k, 1]%2) && 0!=(u%f[k, 1]), (valuation(n, f[k, 1])!=f[k, 2]), 0)); };
isA351554(n) = (0==A351555(n));

Crossrefs

Cf. A000203, A003961.

Positions of zeros in A351555.

Subsequences: A351553 (even terms), A351551, A349169, A349745, also these, at least all the currently (Feb 2022) known terms: A005820, A007691, A046060.

Sequence in context: A345090 A059096 A257678 * A002038 A032501 A240212

Adjacent sequences: A351551 A351552 A351553 * A351555 A351556 A351557

Keyword

nonn

Author

Antti Karttunen, Feb 16 2022

Status

approved