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A353750
a(n) = phi(sigma(n)) * A064989(sigma(n)), where A064989 shifts the prime factorization one step towards lower primes.
12
1, 4, 2, 30, 4, 8, 4, 48, 132, 24, 8, 60, 30, 16, 16, 870, 24, 528, 24, 120, 16, 48, 16, 96, 870, 120, 48, 120, 48, 96, 16, 720, 32, 144, 32, 3960, 306, 96, 120, 288, 120, 64, 140, 240, 528, 96, 32, 1740, 1224, 3480, 96, 1050, 144, 192, 96, 192, 96, 288, 96, 480, 870, 64, 528, 14238, 240, 192, 416, 720, 64, 192, 96
OFFSET
1,2
COMMENTS
In contrast to A353749, this is not multiplicative, except on positions given by A336547.
It seems that a(n) = A353749(n) only on n=1. This would then imply that the intersection of A006872 and A336702 = {1}.
FORMULA
a(n) = A353749(A000203(n)) = A062401(n) * A350073(n).
a(n) = A353749(n) + A353757(n).
PROG
(PARI)
A064989(n) = { my(f=factor(n>>valuation(n, 2))); for(i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f); };
A353750(n) = { my(s=sigma(n)); (eulerphi(s)*A064989(s)); };
CROSSREFS
Cf. A353757, A353758 (where a(n) < A353749(n)), A353759 (where a(n) >= A353749(n)), A353760, A353790 [= a(A003961(n))].
Cf. also A353792.
Sequence in context: A121667 A368767 A291844 * A093991 A030447 A302369
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 07 2022
EXTENSIONS
Dubious comment deleted by Antti Karttunen, Jan 26 2023
STATUS
approved