A337386 Numbers k for which A003973(k) >= 2*A003961(k).

120, 180, 240, 300, 360, 420, 480, 504, 540, 600, 630, 660, 720, 780, 840, 900, 924, 960, 990, 1008, 1020, 1050, 1080, 1092, 1140, 1170, 1200, 1260, 1320, 1380, 1440, 1470, 1500, 1512, 1560, 1620, 1650, 1680, 1740, 1800, 1848, 1860, 1890, 1920, 1980, 2016, 2040, 2100, 2160, 2184, 2220, 2280, 2310, 2340, 2400, 2460

Offset: 1

Author

Antti Karttunen, Aug 27 2020

Keywords

• nonn

Comments

Provided that there are no odd perfect numbers, then these are equal to numbers k for which A003961(k) is in A005231, i.e., numbers that become odd abundant numbers when prime-shifted once.

Not all terms are even. The first odd term is a(8313165) = 334639305 = A064989(A115414(1)). (See A337385). For any odd term x present, A064989(x) is also present, for example, A064989(334639305) = 19399380 = a(482324).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25993; all terms < 2^20
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A003973, A005231, A115414, A336389, A337468.

Subsequence of A005101, of A337381, and of A246282.

Subsequences: A337385 (odd terms), A337479 (primitive elements).

Programs

Mathematica

Select[Range[2500], If[# == 1, 1, DivisorSigma[1, # ]] >= 2# &@ Apply[Times, FactorInteger[#] /. {p_, e_} /; e > 0 :> Prime[PrimePi@ p + 1]^e] &] (* Michael De Vlieger, Aug 27 2020 *)

PARI

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