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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.
8
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.
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 16 2022
STATUS
approved