A355941 Numbers k such that A003973(k) is a multiple of A000203(k).

1, 6, 14, 15, 24, 35, 42, 56, 105, 168, 210, 286, 376, 470, 552, 637, 672, 715, 840, 858, 874, 969, 1144, 1274, 1288, 1410, 1848, 1880, 2001, 2002, 2145, 2185, 2261, 2622, 3021, 3185, 3290, 3296, 3375, 3432, 3496, 3822, 4290, 4669, 4830, 4968, 5005, 5096, 5640, 6118, 6291, 6555, 6783, 7049, 7776, 8008, 9555, 9888

Offset: 1

Author

Antti Karttunen, Jul 22 2022

Keywords

• nonn

Comments

If both x and y are terms and gcd(x, y) = 1, then x*y is a term also.

Links

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

Crossrefs

Cf. A000203, A003973.

Positions of 1's in A355934, and also in A355940 (characteristic function).

Programs

Mathematica

f[p_, e_] := ((q = NextPrime[p])^(e + 1) - 1)/(q - 1); Select[Range[10^4], # == 1 || Divisible[Times @@ f @@@ FactorInteger[#], DivisorSigma[1, #]] &] (* Amiram Eldar, Jul 22 2022 *)

PARI

A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
A355940(n) = !(A003973(n)%sigma(n));
isA355941(n) = A355940(n);