A325378 a(n) = A162296(A228058(n)) - A048250(A228058(n)), where A162296 is the sum of divisors that have a square factor, A048250 the sum of the squarefree divisors, and A228058 lists numbers satisfying Euler's condition for odd perfect numbers.

30, 70, 90, 246, 150, 266, 190, 210, 678, 342, 270, 310, 654, 574, 370, 570, 450, 738, 930, 490, 510, 722, 550, 570, 798, 1582, 690, 1026, 750, 2034, 790, 1230, 1626, 1178, 870, 1526, 910, 970, 990, 2046, 1558, 1406, 1722, 1962, 1150, 1170, 1210, 4062, 1710, 1290, 3390, 1350, 1862, 1390, 1938, 1410, 2214, 1470, 3030

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..25000

Formula

a(n) = A389096(n) - A389164(n) = A162296(A228058(n)) - A048250(A228058(n)).

a(n) = A325319(n) + A325320(n).

a(n) = -A388994(A228058(n)). - Antti Karttunen, Sep 29 2025

Prog

(PARI)
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
k=0; n=0; while(k<100, n++; if(isA228058(n), k++; print1(A162296(n) - A048250(n), ", ")));

Crossrefs

Cf. A048250, A162296, A228058, A325319, A325320, A325379, A388994, A389096, A389164.

Sequence in context: A392780 A112343 A182996 * A164596 A295102 A381736

Adjacent sequences: A325375 A325376 A325377 * A325379 A325380 A325381

Keyword

nonn

Author

Antti Karttunen, Apr 22 2019

Status

approved