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A351456
a(n) = A003958(sigma(A003961(n))), where A003958 is multiplicative with a(p^e) = (p-1)^e, A003961 multiplicative with a(prime(k)^e) = prime(1+k)^e, and sigma is the sum of divisors function.
5
1, 1, 2, 12, 1, 2, 2, 4, 30, 1, 6, 24, 4, 2, 2, 100, 4, 30, 2, 12, 4, 6, 8, 8, 36, 4, 24, 24, 1, 2, 18, 72, 12, 4, 2, 360, 12, 2, 8, 4, 10, 4, 2, 72, 30, 8, 8, 200, 108, 36, 8, 48, 8, 24, 6, 8, 4, 1, 30, 24, 16, 18, 60, 1092, 4, 12, 4, 48, 16, 2, 36, 120, 4, 12, 72, 24, 12, 8, 12, 100, 700, 10, 16, 48, 4, 2, 2, 24
OFFSET
1,3
FORMULA
Multiplicative with a(p^e) = A003958(1 + q + ... + q^e), where q = nextPrime(p) = A151800(p).
a(n) = A351457(n) + A339905(n).
PROG
(PARI)
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351456(n) = A003958(sigma(A003961(n)));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Feb 12 2022
STATUS
approved