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

1,1

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)

Formula

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

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 *)

Prog

(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)));

Crossrefs

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

Cf. also A071395, A091191, A337372, A337543.

Sequence in context: A204828 A204830 A279088 * A322377 A247851 A179232

Adjacent sequences: A337476 A337477 A337478 * A337480 A337481 A337482

Keyword

nonn

Author

Antti Karttunen, Sep 01 2020

Status

approved