A332229 Even numbers k such that A156552(k) is not a power of prime, and for which A323243(k) = sigma(A156552(k)) is congruent to 2 modulo 8.

290, 434, 550, 826, 858, 1394, 1798, 2254, 2418, 2546, 2950, 3094, 3910, 4150, 4382, 4930, 5590, 6138, 6358, 6390, 6710, 6966, 7514, 7546, 7622, 7658, 7990, 8550, 8798, 8906, 9230

Offset: 1

Author

Antti Karttunen, Feb 13 2020

Keywords

• nonn

Comments

Numbers k for which A156552(k) is in A332228.

Sequence A005940(1+A332228(n)), n >= 1, sorted into ascending order.

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A005940, A156552, A323243, A332225, A332228.

Subsequence of A324814.

Programs

PARI

A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
isA332228(n) = ((n%2)&&!isprimepower(n)&&2==(sigma(n)%8));
isA332229(n) = isA332228(A156552(n));

PARI

v156552sigs = readvec("a156552.txt"); \\ Factorization file for A156552 prepared by Hans Havermann, available at https://oeis.org/A156552/a156552.txt
isA156552not_a_primepower(n) = if(n<=2,0,my(prsig=v156552sigs[n]); length(prsig[1])>1);
A323243(n) = if(n<=2,n-1,my(prsig=v156552sigs[n],ps=prsig[1],es=prsig[2]); prod(i=1,#ps,((ps[i]^(1+es[i]))-1)/(ps[i]-1)));
isA332229(n) = (!(n%2)&&isA156552not_a_primepower(n)&&(2==(A323243(n)%8)));
k=0; for(n=1,10000,if(isA332229(n),k++; print1(n,", ")));