A351547 a(n) = sigma(n) / A351545(n).

1, 1, 4, 7, 6, 4, 8, 15, 13, 2, 12, 28, 14, 8, 24, 31, 18, 13, 20, 6, 32, 4, 24, 12, 31, 14, 40, 56, 30, 8, 32, 63, 48, 2, 48, 91, 38, 20, 56, 90, 42, 32, 44, 84, 78, 8, 48, 124, 57, 31, 72, 98, 54, 40, 72, 120, 16, 10, 60, 24, 62, 32, 104, 127, 12, 16, 68, 14, 96, 16, 72, 195, 74, 38, 124, 140, 96, 56, 80, 186, 121

Offset: 1

Author

Antti Karttunen, Feb 16 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A351545, A351546, A354997.

Cf. A286385, A342671, A349161, A349162.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351547(n) = { my(s=sigma(n),f=factor(s),u=A003961(n)); s/prod(k=1,#f~,if(!(u%f[k,1]) && (f[k,2]>=valuation(u,f[k,1])), f[k,1]^f[k,2], 1)); };

Formula

a(n) = A000203(n) / A351545(n).

a(n) = A351546(n) * A354997(n). - Antti Karttunen, Jul 09 2022