A337479 Primitive elements of A337386: numbers k for which sigma(A003961(k)) >= 2*A003961(k), but none of the proper divisors of k satisfy the same condition.

120, 180, 300, 420, 504, 630, 660, 780, 924, 990, 1020, 1050, 1092, 1140, 1170, 1380, 1470, 1650, 1740, 1860, 2220, 2310, 2460, 2580, 2730, 2820, 2856, 3168, 3180, 3192, 3432, 3540, 3570, 3660, 3864, 3990, 4020, 4260, 4284, 4290, 4380, 4488, 4590, 4740, 4752, 4788, 4830

Offset: 1

Author

Antti Karttunen, Sep 01 2020

Keywords

• nonn

Comments

Equivalently, numbers k such that A003961(k) is in A006039, i.e., numbers that become an (odd) primitive nondeficient number when prime-shifted once.

Conjecture: every positive integer is either a (possibly trivial) multiple of a sequence term or divides infinitely many terms of this sequence. - Peter Munn, Sep 24 2020

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16350; terms less than 2^25
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A003973, A006039, A337386, A337539, A337690.

Cf. also A071395, A091191, A337372, A337543.

Programs

Mathematica

Block[{f}, f[1] = 1; f[n_] := Times @@ Map[#1^#2 & @@ # &, FactorInteger[n] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}]; Select[Range[5000], And[DivisorSigma[1, Last[#]] >= 2 Last[#], NoneTrue[Most[#], DivisorSigma[1, #] >= 2 # &]] &@ Map[f, Divisors@ #] &] ] (* Michael De Vlieger, Oct 05 2020 *)

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA337386(n) = { my(x=A003961(n)); (sigma(x)>=2*x); };
isA337479(n) = (1==sumdiv(n,d,isA337386(d)));

Formula

For all n >= 1, A337690(a(n)) = A337539(n).