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A351449
a(n) = A064989(A295294(A003961(n))).
3
1, 1, 1, 11, 1, 1, 1, 3, 29, 1, 1, 11, 1, 1, 1, 49, 1, 29, 1, 11, 1, 1, 1, 3, 34, 1, 22, 11, 1, 1, 1, 55, 1, 1, 1, 319, 1, 1, 1, 3, 1, 1, 1, 11, 29, 1, 1, 49, 85, 34, 1, 11, 1, 22, 1, 3, 1, 1, 1, 11, 1, 1, 29, 1091, 1, 1, 1, 11, 1, 1, 1, 87, 1, 1, 34, 11, 1, 1, 1, 49, 469, 1, 1, 11, 1, 1, 1, 3, 1
OFFSET
1,4
FORMULA
Multiplicative with a(p) = 1 and for e > 1, a(p^e) = A064989((q^(e+1)-1)/(q-1)), where q = nextPrime(p) = A151800(p).
a(n) = A326042(n) / A351451(n).
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); }; \\ From A057521
A064989(n) = { my(f = factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A295294(n) = sigma(A057521(n));
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Feb 11 2022
STATUS
approved