A353746 Numbers k for which phi(sigma(k)) + A064989(sigma(k)) is equal to phi(k) + A064989(k).

1, 114, 618, 2428, 3868, 11706, 16012, 23946, 2031108, 2938902, 3531102, 10475862, 98250486, 205600756

Offset: 1

Author

Antti Karttunen, May 06 2022

Keywords

• nonn
• more

Comments

Numbers k such that A353747(k) = A353747(sigma(k)), or equally that A062401(k) + A350073(k) = A000010(k) + A064989(k).

When A003961(x) is substituted for k, the condition becomes: numbers x such that phi(A003973(x))+A326042(x) = A003972(x)+x, i.e. A353747(A003973(x)) - x = A003972(x).

a(15) > 1442840576, if it exists.

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000010, A000203, A062401, A064989, A350073, A353747.

Cf. A003961, A003972, A003973, A326042.

Cf. also A348748, A348749, A351440.

Programs

PARI

A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
isA353746(n) = { my(s=sigma(n)); ((eulerphi(s)+A064989(s))==(eulerphi(n)+A064989(n))); };