A332229 - OEIS

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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

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

OFFSET

1,1

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..31.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

PROG

(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, ", ")));

CROSSREFS

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

Subsequence of A324814.

Sequence in context: A186553 A075420 A075421 * A296055 A090839 A158255

Adjacent sequences: A332226 A332227 A332228 * A332230 A332231 A332232

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 13 2020

STATUS

approved