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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. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 28 15:20 EST 2022. Contains 350657 sequences. (Running on oeis4.)