A337045 Indecomposable sigma-powerful numbers: powerful numbers k such that sigma(k) is also powerful, but restricted to terms that are not the product of 2 terms > 1 of A337044.

81, 343, 400, 9261, 189728, 224939, 972000, 1705636, 2205472, 3087000, 3591200, 3648100, 7968032, 13645088, 15350724, 21161304, 24240600, 25992000, 26680500, 29184800, 32832900, 48586824, 51595489, 80802000, 103617387, 109215352, 110215125, 119604096, 122805792

Offset: 1

Author

Hugo Pfoertner, Aug 15 2020

Keywords

• nonn

Comments

This is an implementation of the suggestion that Walter A. Kehowski made on his website (see link) with regard to so-called indecomposable sigma-powerful numbers. However, the results deviate from the table linked there. The table is considered to be deficient.

Examples

			From _David A. Corneth_, Aug 29 2020: (Start)
No two proper divisors of 400 are sigma-powerful and have the product of those divisors 400 so 400 is in the sequence.
27783 = 81 * 343 is sigma-powerful but 81 and 343 are sigma-powerful as well so 27783 can be decomposed into two sigma-powerful factors. So 27783 is not in the sequence. (End)
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..6421 (terms < 10^18)
• Walter A. Kehowski, Sigma-powerful numbers, Aug 09 2010.

Crossrefs

Cf. A000203, A001694, A128607, A180090, A337044.

Programs

PARI

v=vector(50); n=0;
for(m=2, 150000000, my(is); if(ispowerful(m) && ispowerful(sigma(m)), v[n++]=m; is=1; for(j=1, n-1, if(v[n]%v[j], , if(vecsearch(v[1..n-1], v[n]/v[j]), is=0; break))); if(is, print1(v[n], ", "))))