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A351442
a(n) = A003958(sigma(n)), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.
13
1, 2, 1, 6, 2, 2, 1, 8, 12, 4, 2, 6, 6, 2, 2, 30, 4, 24, 4, 12, 1, 4, 2, 8, 30, 12, 4, 6, 8, 4, 1, 24, 2, 8, 2, 72, 18, 8, 6, 16, 12, 2, 10, 12, 24, 4, 2, 30, 36, 60, 4, 36, 8, 8, 4, 8, 4, 16, 8, 12, 30, 2, 12, 126, 12, 4, 16, 24, 2, 4, 4, 96, 36, 36, 30, 24, 2, 12, 4, 60, 100, 24, 12, 6, 8, 20, 8
OFFSET
1,2
COMMENTS
Question: Are there more fixed points than 1, 2, 8, 128, 288, 720, 32768, 29719872, ..., 2147483648 ?
FORMULA
Multiplicative with a(p^e) = A003958(1 + p + ... + p^e).
a(n) = A003958(A000203(n)).
a(n) = A351444(n) - A322582(n) = A351445(n) + A003958(n).
PROG
(PARI)
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A351442(n) = A003958(sigma(n));
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Feb 12 2022
STATUS
approved